Abstract : Two main topics are discussed in the report. One is a necessary and sufficient condition for two symmetric matrices to be realized as the terminal capacity matrix (TCM) and the expected value terminal capacity matrix (EVTCM) of a tree communication net. The other one is concerned with a necessary and sufficient condition for a symmetric matrix to be realizable as the EVTCM of a tree net. It is shown that there exists a certain tree net which can never be equivalent to a non-tree net under the same TCM and EVTCM, except when all edges of both nets have reliability one. A necessary and sufficient conditon is given for a matrix to be realizable as the reliability matrix (RM) of a tree net. Although the RM is a special case of the first topic, it plays an important role in the EVTCM of a tree. It is proved that if a matrix whose nondiagonal elements are less than one is realizable as the RM of a tree, its topology is unique. Making use of the realiability matrix, a necessary and sufficient conditon for the first problem is developed. (Modified author abstract)